Can anyone help me solve this question?

The net cost of the amount needed in filling the prescription is 7.86 per gallon

Net cost = 12 - (34.5% of 12)

= 12 - (0.345 × 12)

= 12 - 4.14

= 7.86 per gallon

Therefore the net cost of the amount needed in filling the prescription is 7.86 per gallon

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Answer:

(B). roots

Step-by-step explanation:

(a ± b)² = a² ± 2ab + b²

~~~~~~~~

( [tex]\sqrt{4x+5}[/tex] - [tex]\sqrt{x-1}[/tex] )² = ( [tex]\sqrt{x+4}[/tex] )²

( [tex]\sqrt{4x+5}[/tex] )² - 2[tex]\sqrt{(4x+5)(x-1)}[/tex] + ( [tex]\sqrt{x-1}[/tex] )² = ( [tex]\sqrt{x+4}[/tex] )²

4x + 5 - 2[tex]\sqrt{(4x+5)(x-1)}[/tex] + x - 1 = x + 4

2[tex]\sqrt{(4x+5)(x-1)}[/tex] = 4x + 5 + x - 1 - x - 4

[tex]\sqrt{(4x+5)(x-1)}[/tex] = 2x

( [tex]\sqrt{(4x+5)(x-1)}[/tex] )² = ( 2x )²

( 4x + 5 )( x - 1 ) = 4x²

4x² + x - 5 = 4x² ⇒ x = 5

Answer:

x = -36

Step-by-step explanation:

x/4 + 10 = 1

To solve this two step equation, first subtract 10 from each side.

x/4 + 10 -10 = 1-10

x/4 = -9

Then multiply each side by 4 to isolate x

x/4 * 4 = -9*4

x = -36

The width of the rectangle is 6.82 meters, while the length of the rectangle is 8.184 meters.

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.

Let the width of the rectangle be x.

Given that a rectangular room is 1.2 times as long as it is wide. Therefore, the length is 1.2x.

Perimeter = 2(x + 1.2x)

30 meters = 2(2.2x)

30 = 4.4x

x = 6.82

Hence, the width of the rectangle is 6.82 meters, while the length of the rectangle is 8.184 meters.

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Volume is a three-dimensional scalar quantity. The length of the square base side is 5 meters.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of the square pyramid is one-third of the product of the base area and the height. Therefore, the area of the base of the pyramid will be,

The volume of pyramid = (1/3) × Height × (Base length)²

75 m³ = (1/3) × 9 × (Base length)²

Base length)² = 25 m²

Base length = 5 m

Hence, the length of the square base side is 5 meters.

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Draw the graph:

f(x) = |x-1|

f(x) = -(x-1) when x-1 is negative

f(x) = (x-1) when x-1 is positive

when x = -2, f(x) = 3

when x = -1, f(x) = 2

when x = 0, f(x) = 1

when x = 1, f(x) = 0

when x = 2, f(x) = 1

Using this values, draw the graph of f(x) = |x-1|

Hence, the required modulus of x-1 graph.

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Answer:

$1756

Step-by-step explanation:

1.  More = Addition

2. Twice = Multiplication by 2

3. Tuition costs $100 more than twice room and board

   Tuition = 2x + 100

   $2584 = (2x + 100) + x

   $2584 = 3x + 100

4. Subtract 100 on both sides: $2484 = 3x

5. Divide both sides by 3: $828 = x

6. Plug it in to the tuition equation: Tuition = 2(828) + 100

                                                                       = $1756

Check Work: (828*2) + 100 = $1756

                      $1756 + 828  = $2584

Take any two pairs of the given points and make vectors out of them. For example, the vector from A to B is

[tex]\vec v_1 = \langle 1,4,5\rangle - \langle 1,1,1\rangle = \langle0,3,4\rangle[/tex]

and the vector from A to C is

[tex]\vec v_2 = \langle -3,-2,0\rangle - \langle1,1,1\rangle = \langle-4,-3,-1\rangle[/tex]

These vectors lie in the same plane (the one we want). We can get a third vector that is normal to the plane by taking their cross product (details omitted).

[tex]\vec n = \vec v_1 \times \vec v_2 = \langle 9,-16,12 \rangle[/tex]

If [tex]\vec u = \langle x,y,z\rangle[/tex] is an arbitrary vector, then the vector from any of the points A, B, or C to [tex]\vec u[/tex] will lie in our plane. That is, if we start from A,

[tex](\vec u - \langle1,1,1\rangle) \cdot \vec n = 0[/tex]

and this reduces to the equation of the plane,

[tex]\langle x - 1, y - 1, z - 1 \rangle \cdot \langle 9, -16, 12 \rangle = 0[/tex]

[tex]9 (x - 1) - 16 (y - 1) + 12 (z - 1) = 0[/tex]

[tex]\boxed{9x - 16y + 12z = 5}[/tex]

This follows immediately from the cross product identity

[tex]\|\vec x \times \vec y\| = \|\vec x\| \|\vec y\| \sin(\theta)[/tex]

where [tex]\theta[/tex] is the angle between [tex]\vec x[/tex] and [tex]\vec y[/tex]. The left side corresponds to the area of the parallelogram spanned by [tex]\vec x[/tex] and [tex]\vec y[/tex]; half of this area would be that of a triangle. (see attached)

In our case, we have

[tex]\|\vec n\| = \|\vec v_1 \times \vec v_2\| = \sqrt{481}[/tex]

so the area of ABC is [tex]\boxed{\dfrac{\sqrt{481}}2}[/tex].

We already know the first vector, [tex]v_1[/tex].

The vector from C to B is

[tex]\vec v_3 = \langle 1,4,5 \rangle - \langle -3,-2,0 \rangle = \langle 4, 6, 5 \rangle[/tex]

Recall the dot product identity,

[tex]\vec x \cdot \vec y = \|\vec x\| \|\vec y\| \cos(\theta)[/tex]

Then

[tex]\vec v_1 \cdot \vec v_3 = \|\vec v_1\| \|\vec v_3\| \cos(\theta) \implies \cos(\theta) = \dfrac{38}{5\sqrt{77}} \implies \theta \approx \boxed{29.9914^\circ}[/tex]

Answer:

Step-by-step explanation:

cos (x/2)=cos x+1

cos (x/2)=2cos ²(x/2)

2 cos²(x/2)-cos (x/2)=0

cos (x/2)[2 cos (x/2)-1]=0

cos (x/2)=0=cos π/2,cos (3π/2)=cos (2nπ+π/2),cos(2nπ+3π/2)

x/2=2nπ+π/2,2nπ+3π/2

x=4nπ+π,4nπ+3π

n=0,1,2,...

x=π,3π

or x=180°,540°,...

180°∈[0,360]

so x=180°

or

2cos(x/2)-1=0

cos (x/2)=1/2=cos60,cos (360-60)=cos 60,cos 300=cos (360n+60),cos (360n+300)

x/2=360n+60,360n+300

x=720n+120,720n+300

n=0,1,2,...

x=120,300,840,1020,...

only 120° and 300° ∈[0,360°]

Hence x=120°,180°,300°

Answer:

Step-by-step explanation:

Answer:

4 5/18 ≈ 4.278

Step-by-step explanation:

1/2 of 8 5/9

8 5/9 = 77/9

1/2 x 77/9

= 77 over 18

= 77/18

= 4 and 5/18

≈ 4.278

Hope this helps!

Answer:

no because 1 x value cannot have 2 y values , i hope the helps

Choose C.

Answer: 754

Step-by-step explanation:

Divide 683/11 to get the unit rate of 58. That means she is driving 58mph.

Multiply that by how many hours you have, 13, and you get 754.

0.3:0.1

Step-by-step explanation:

first convert the % to decimals.

75%=0.75

25%=0.25

then look for a common factor and divide be that, in this case its 5.

0.75/5=0.15

0.25/5=0.5

now since these arent in the simplified form, you gotta divide again by 5.

0.15/5=0.3

0.5/5=0.1

The ratio to adults to children is 3:1

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

75% of the people are adults and 25% are children.

So, the ratio of adult to children

= (75%) / (25%)

= 0.75 / 0.25

= 75/25

= 3/1

Hence, the ratio to adults to children is 3:1

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Answer:

C. [tex]1\frac{1}{2} x - 1\frac{3}{4}[/tex]

Step-by-step explanation:

c

Answer:

[tex]1\frac{1}{2}x - 1\frac{3}{4}[/tex]

Step-by-step explanation:

So the first step is to distribute the [tex]\frac{1}{4}[/tex] to the (3x - 7) this gives you:

[tex]\frac{3}{4}x-\frac{7}{4} + \frac{3}{4}x[/tex]

Add like terms:

[tex]\frac{6}{4}x-\frac{7}{4}[/tex]

Simplify the fractions:

[tex]\frac{3}{2}x-\frac{7}{4}[/tex]

Convert it to a mixed fraction:

[tex]1\frac{1}{2}x - 1\frac{3}{4}[/tex]

The total finance charge is $611.20 (Option c) for this compound interest.

Data Given

Principal, P = $4250

Rate of Compound Interest, R = 13.25%

Time, t = 24 months, i.e., 2 years

Since it is compounded monthly, n = 12

Calculating the Total Finance Charge

We know that the formula for total amount of finance charge in a Compound Interest is,

[tex]A=P\frac{r(1+r)^{n} }{(1+r)^{n} - 1}[/tex]

Substituting the values of P, R and n, we get,

[tex]A=4250\frac{13.25(1+13.25)^{24} }{(1+13.25)^{24} - 1}[/tex]

[tex]A = 611.20[/tex]

Thus, the total finance charge is $611.20

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The graph of R intersects with the horizontal or oblique asymptote at (-3, 0)

The function is given as:

[tex]R(x)=\frac{x+3}{x\left(x+8\right)}[/tex]

Set the numerator to 0

[tex]R(x)=\frac{0}{x\left(x+8\right)}[/tex]

Evaluate

R(x) = 0

This means that the horizontal asymptote of R(x) is y = 0

The function is given as:

[tex]R(x)=\frac{x+3}{x\left(x+8\right)}[/tex]

The numerator has a degree of 1, while the denominator has a degree of 2

When the degree of the numerator is less than the degree of denominator, then the function has no oblique asymptote

Hence, the function has no oblique asymptote.

In (a), we have:

R(x) = 0

Substitute R(x) = 0 in [tex]R(x)=\frac{x+3}{x\left(x+8\right)}[/tex]

[tex]\frac{x+3}{x\left(x+8\right)} = 0[/tex]

Cross multiply

x + 3 = 0

Solve for x

x = -3

So, we have:

(x, y) = (-3, 0)

Hence, the graph of R intersects with the horizontal or oblique asymptote at (-3, 0)

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The linear equation passes through (0, -4) and (1, 0), so we conclude that the correct option is the first one.

Here we have the linear equation:

y - 6 = 4*(x - 3) + 2

if we rewrite the line in slope-intercept form, we get:

y = 4x - 12 + 2 + 6

y = 4x - 4

Then the y-intercept of the line is (0, -4). And when x = 1, we have:

y = 4*1 - 4 = 0

So the line also passes through (1, 0).

Then the correct option is the first one:

"Number graph ranging from negative four to three on the x-axis and negative five to two on the y-axis. A line is drawn on the graph that passes through the points (zero, negative four) and (one, zero)."

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Answer:

operator

Step-by-step explanation:

Operator is represented as any symbol that indicates an operation to be performed.

Examples:

- Square root of√x, which indicates the square root is to be taken

- d/dx, which indicates differentiation with respect to x is to be performed

Answer:

OPERATION

OF ALGEBRA IN MATH

When t is between 2 and 5, the ball will be above 10 feet.so answer is:

C. 2 ≤ t ≤ 5

Given, height h(t) = ₋t² ₊ 7t

At what values of time t is the ball 10 feet above the ground = ?

To find out the time we need to set up an inequality.

Inequality expression is given as = ₋t² ₊ 7t ≥ 10

                                                       = ₋t² ₊ 7t ₋ 10 ≥ 0

                                                       = ₋(t² ₋ 7t ₊ 10) ≥ 0

                                                       = t² ₋ 7t ₊10 ≥ 0

Now, factorize the expression and get the factors.

= t² ₋ 2t ₋ 5t ₊ 10 ≥ 0

=t(t ₋ 2) ₋ 5(t ₋ 2) ≥ 0

=(t ₋ 2) (t ₋ 5) ≥ 0

Hence t value ranges from t = 2 and 5.

As a result, when t is between 2 and 5 seconds, the ball will be farther than 10 feet, 2 ≤ t ≤ 5

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The area of the shaded triangle BDE is 4 cm²

The area is the amount of space within the perimeter of a 2D shape.

area of ΔADE= / *b *h

=1/2 * 8 *5

= 20 cm²

area of ΔBCD

= 26-20

= 6 cm²

area of CDE

= 1/2* 5 * 4

= 10 cm²

Area of shaded triangle,

=10-6

=4 cm²

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The value of the hypotenuse is C = 11.73

We can see that C is the hypotenuse of the right triangle.

We can see that the top angle measures 43°, and the opposite cathetus to that angle measures 8 units.

Then we can use the rule:

Sin(a) = (opposite cathetus)/(hypotenuse).

Replacing what we know:

Sin(43°) = 8/C

Solving for C:

C = 8/Sin(43°) = 11.73

The value of the hypotenuse is C = 11.73

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The true statement is (b) use of incorrect header

The product expression is given as:

(-2x - 1)(2x - 1)

Expand the expression

(-x - x - 1)(x + x - 1)

This means that the header of the algebra tiles would be:

-x, -x, 1 and x, x and -1

From the figure, we can see that this is incorrectly represented

Hence, the true statement is (b)

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Answer:

refer to the above attachment

Answer :

X*2-16

Explanation :

The square of x is x*2 and the square of 8 is 64

a. The probability of rolling a sum of 7 or 11. (sum of 7 or 11) is 2/9. b. the probability of not rolling a sum of 7 nor 11. (not sum of 7 nor 11) is 7/9.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The probability of getting a total of 7 = 6/36

The probability of getting total of 11 = 2/36

a. The probability of rolling a sum of 7 or 11. (sum of 7 or 11)

= 6/36 + 2/36

= 2/9

b. Find the probability of not rolling a sum of 7 nor 11. (not sum of 7 nor 11)

= 1- 2/ 9

= 7/9

c. Find the odds against rolling a sum of 7 or 11.

= 2/9

d. The money you will win, If you make a $10 bet that you will roll a sum of 7 or 11, and the dice land on a sum of 7 or 11.

10 x  2/9 = 20/9

10 x 7/9 = 70/9

Thus, The money you will win $10.

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The area of the shaded region for a z-score of -0.92 is 0.1788, which means the area that will be shadeded in the normal distribution graph is 17.88% of the total.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.

1.) The area of the shaded region for a z-score of -0.92 is 0.1788, which means the area that will be shadeded in the normal distribution graph is 17.88% of the total.

2.) The area of the shaded region for a z-score of 1.23 is 0.8907, which means the area that will be shadeded in the normal distribution graph is 89.07% of the total.

Now, the area of the shaded region will be,

Area = 0.8907 - 0.1788

        = 0.7119

        = 71.19%

Hence, the area of the shaded region is 71.19%.

The complete question is mentioned in the below image.

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Answer:

a. n+5

b. n+ 7

c. 1\2(n×2n)

d. n +n+1 n+2

Hello!

Let the missing number be x.

⇒ 3 1/3 × x = 8

⇒ 10/3 × x = 8

⇒ x = 24/10

⇒ x = 12/5

The other number is [tex]\boxed {\frac{12}{5}}[/tex]

Answer:

The other number ia:

12/5

Step-by-step explanation:

3 1/3 = 3 + 1/3 = 9/3 + 1/3 = 10/3

a * 10/3 = 8

a = 8*3/10

a = 24/10

a = 12/5

a = 2.4

Check:

(12/5) * (10/3) = 8

(12*10) / (5*3) = 8

120 / 15 = 8